*Let’s move from top to bottom: MULTIPLES OF 3 AND 5: Multiples of 3 and 5 are multiples of 15 The number of elements in A = the integer part of (1000/21) – 9 = 47 – 9 = 38 Now our diagram looks like this: Almost there…*remember not to double count the portions of the diagram that are already labeled!Problem Mat - print out on A3 double sided and you have a collection of Venn diagram questions students can attempt.

Data science courses contain math—no avoiding that!

This course is designed to teach learners the basic math you will need in order to be successful in almost any data science math course and was created for learners who have basic math skills but may not have taken algebra or pre-calculus.

Almost all combinatorics problems can be solved with a single tool that can be used in two different ways – one way when order matters, and another way when order doesn’t matter.

However sometime it pays to take a different approach.

All of these problems can be solved with Venn diagrams 1.

How many positive integers less than 1,000,000 are neither squares nor cubes? Given a random 6-digit integer, what is the probability that the product of the first and last digit is even?

This trick or trap comes up a lot in combinatorics problems.

It’s called “double counting.” To avoid this problem we can use Venn diagrams.

MULTIPLES OF 3 AND NOT 5 OR 7: The number of elements in A = the integer part of (1000/7) – (9 19 38) = 142 – 66 = 76 Our final diagram: So the number of elements less than 1000 which are divisible by 3, 5 or 7 = 248 96 76 19 57 38 9 = 543 And the number of elements less than 1000 which are NOT divisible by 3, 5, nor 7 = 1000 – 543 = 457 The answer is (A).

Keep in mind I’m going to leave you with some challenging problems to try on your own.

## Comments Problem Solving Using Venn Diagrams

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